Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT

Patrick M. Gilmer; Xuanye Wang

doi:10.1090/s0002-9939-2014-12022-3

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arXiv · 1201.1921

Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT

Patrick M. Gilmer·Xuanye Wang

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Abstract

A TQFT is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2+1-cobordism category is built from manifolds which are equipped with an extra structure such as a p_1-structure, or an extended manifold structure. We perform the universal construction of Blanchet, Habegger, Masbaum and Vogel on a cobordism category without this extra structure and show that the resulting quantization functor assigns an infinite dimensional vector space to the torus.

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BibTeX RIS

Patrick M. Gilmer, Xuanye Wang. 2012-01-09. Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT. https://doi.org/10.1090/s0002-9939-2014-12022-3

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